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dc.contributor.authorCarvajal, Orlando Aen 14:19:53 (GMT) 14:19:53 (GMT)
dc.description.abstractThis work presents a new hybrid symbolic-numeric method for fast and accurate evaluation of multiple integrals, effective both in high dimensions and with high accuracy. In two dimensions, the thesis presents an adaptive two-phase algorithm for double integration of continuous functions over general regions using Frederick W. Chapman's recently developed Geddes series expansions to approximate the integrand. These results are extended to higher dimensions using a novel Deconstruction/Approximation/Reconstruction Technique (DART), which facilitates the dimensional reduction of families of integrands with special structure over hyperrectangular regions. The thesis describes a Maple implementation of these new methods and presents empirical results and conclusions from extensive testing. Various alternatives for implementation are discussed, and the new methods are compared with existing numerical and symbolic methods for multiple integration. The thesis concludes that for some frequently encountered families of integrands, DART breaks the curse of dimensionality that afflicts numerical integration.en
dc.format.extent588541 bytes
dc.publisherUniversity of Waterlooen
dc.rightsCopyright: 2004, Carvajal, Orlando A. All rights reserved.en
dc.subjectComputer Scienceen
dc.subjectMultiple Integrationen
dc.subjectGeddes Seriesen
dc.subjectSymbolic-Numeric Integrationen
dc.titleA Hybrid Symbolic-Numeric Method for Multiple Integration Based on Tensor-Product Series Approximationsen
dc.typeMaster Thesisen
dc.pendingfalseen of Computer Scienceen
uws-etd.degreeMaster of Mathematicsen

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